\section{Why Does Insurance Work?} 
\label{sec:WhyInsuranceWorks} 

The Central Limit Theorem (CLT) (Hogg and Craig, 1978; Hogg and Klugman, 1984) explains that insurance works because large insurers issue many policies, and the year to year, or portfolio to portfolio, variation in average claim costs approaches population average costs as portfolio sizes increase. Large insurers costs are very predictable, while small insurers tend to earn excessive profits, or incur excessive losses, each year. This exposure to high and low losses is the hallmark of insurer inefficiency. Inefficient insurers, including risk assuming health care providers, are more likely to struggle financially and become insolvent, as has happened for the last forty years (Mayes, 2005).

%As a simple example, suppose the average loss ratio for a population is 0.7500, and insurers devote 15\% of their premiums to no claim expenses. A very large insurer may have a loss ratio that falls between 0.7300 and 0.7700 in 99 out of 100 years. A much smaller insurer, insuring 1\% as many policyholders, will have a loss ratio that varies between 0.5500 and 0.9500 in 99 out of 100 years. The large insurer can meet the highest level of losses it is likely to incur (0.7700), out of currently available premiums (85\% of premium not devoted to non-loss expenses). The smallest insurer would need significant amounts of cash, before issuing policies, to be able to meet its obligations to policyholders and claimants at a loss ratio of 0.9500, which would result in an operating loss of 10\% of revenues. 

Despite the greater efficiency of large insurers, most health care (finance) reform recommendations ignore the CLT. Capitation advocates and other health care reformers suggest the opposite effect, that increased competition, among many small insurers will increase health care (finance) system efficiency and consumer benefits. This is demonstrably false. Limited competition among very few, very large, and very efficient insurers would definitely be more efficient and would yield higher policyholder benefits than large numbers of very small, very inefficient insurers (See Section~\ref{sec:InsurerRiskandMaximumSustainableBenefits}).